BenfordTests (version 1.2.0)

signifd: First Digits Function

Description

Applies the first digits function to each element of a given vector.

Usage

signifd(x = NULL, digits = 1)

Arguments

x

A numeric vector.

digits

An integer determining the number of first digits to use for testing, i.e. 1 for only the first, 2 for the first two etc.

Value

• Returns a vector of integers the same length as the input vector x.

Details

The first digits function can be written as: $$D_k(x) = \lfloor |x| \cdot 10^{\left( -1 \cdot \lfloor log_{10}|x| \rfloor + k -1 \right)}\rfloor$$ with $k$ being the number of first digits that should be extracted. x is a numeric vector of arbitrary length. Unlike other solutions, this function will work reliably with all real numbers.

References

Joenssen, D.W. (2013) Two Digit Testing for Benford's Law. Proceedings of the ISI World Statistics Congress, 59th Session in Hong Kong. [available under http://www.statistics.gov.hk/wsc/CPS021-P2-S.pdf]

See Also

chisq.benftest; ks.benftest; usq.benftest; mdist.benftest; edist.benftest; meandigit.benftest; jpsq.benftest

Examples

#Set the random seed to an arbitrary number
set.seed(421)
#Create a sample satisfying Benford's law
X<-rbenf(n=20)
#Look at the first digits of the sample
signifd(X)
#should be:
#[1] 6 1 5 2 7 5 7 4 3 1 2 2 1 5 6 2 2 3 1 3